This thesis presents procedures of the multigrid method using unstructured grids for solutions of inviscid compressible flows. The work concentrates on the components of the procedures, such as flow solvers (smoothers), intergrid interpolation, multigrid cycles, nested iterations and data structures. The performance and comparison of different smoothers are in particular emphasised. Some related aspects, e.g. the boundary treatment, are also discussed. Several two dimensional examples, for problems of external and internal inviscid compressible flows, are given to demonstrate the ability of the methods in improving the efficiency of simulating steady compressible flows.